³ò /SKc@s‘dZddkZddkZddkZddkZddkZdefd„ƒYZdefd„ƒYZ defd„ƒYZ d „Z dS( s‡ nmr.py - a library of nmr routines classes: nmr.Trace, nmr.Spectrum, nmr.SignalMismatchError function: nmr.rfftfreq 7 Dec 2009, Lev iÿÿÿÿNtSignalMismatchErrorcBs&eZdZddd„Zd„ZRS(s’ Exception raised when incompatible signals are combined. If not None, 'self.signal1' and 'self.signal2' are the signals in question. cCs||_||_dS(ss Exception constructor. Two arguments can be specified, containing two signals in question N(tsignal1tsignal2(tselfRR((sc:\py\lib\nmr.pyt__init__2s cCsdS(NsSignal mismatch((R((sc:\py\lib\nmr.pyt__str__:sN(t__name__t __module__t__doc__tNoneRR(((sc:\py\lib\nmr.pyR,stTracecBs*eZdZd0d„Zd„Zd„Zd„Zd„Zd„Z d„Z d„Z d „Z d „Z d „Zd „Zd „Zd„Zd„Zd„ZeZeZeZd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zdddddddd„Z d„Z!d0d0d„Z"dd0d„Z#e$dd „ƒZ%e$dd!„ƒZ&e$dd"„ƒZ'e$d#„ƒZ(e$d$„ƒZ)e$d%„ƒZ*d0d&„Z+d'e,i-d(„Z.d0d0d0d0d)„Z/d0d0d*„Z0d0d0d+„Z1d,„Z2d-„Z3d.„Z4d0d0dd/„Z5RS(1sW Time domain signal trace. An array of samples is stored at 's', 'dt' is the sampling interval. Timeline is returned by 't()'. Arithmetic operations +,-,*,/ are supported. Other signals or numbers can be added and subtracted. A signal can be multiplied or divided by a number. '&' appends samples to a trace. An array of samples can be concatenated, or another trace. The latter must the same 'dt' as the trace being extended. Also samples can be added to the beginning of a trace. '[t]' returns a sample at the moment 't', time is rounded down. Negative 't' is interpreted as time relative to the end of the trace. IndexError is raised if t is out of range. 'info', set by default to 'None' is intended for metadata related to the trace, such as a record from a scope log. cCs|djoX|d|dt|ƒd}titi|dd…dfƒdtiƒ|_nˆtiti|ƒdtiƒ|_ti|ƒo |}nJt|ƒt|ƒjotdƒ‚n|d|dt|ƒd}titi|ƒƒ|_ d|_ dS( sU Create a time domain signal trace. Takes 1 or 2 arguments. If a single argument is supplied, it is expected to be a two-column array, first column - timeline, second column - samples. If two arguments are supplied, the first is a timeline if it is an array or a timebase if it is a scalar, the second argument is an array of samples. All supplied arrays are copied (so a modification of .s will not affect an array used to create a Trace. If complex numbers are given, imaginary part is discared. iÿÿÿÿiiNtdtypes.time and sample arrays are of different lenght(iÿÿÿÿi(ii( R tlentnumpytasarraytrealtfloat64tstisscalart ValueErrortdttinfo(Rtarg1targ2R((sc:\py\lib\nmr.pyRRs  8$  cCs t|iƒS(sReturn number of samples(R R(R((sc:\py\lib\nmr.pyt__len__oscCs|it|ƒS(sÇ Return time over which samples span [s]. This includes one 'dt' after the last sample, or one might think of it as 'dt/2' before the first and after the last sample. (RR (R((sc:\py\lib\nmr.pyttimespansscCstit|iƒƒ|iS(sReturn timeline array(R tarangeR RR(R((sc:\py\lib\nmr.pytt{scCs d|iS(sReturn sampling rate [Hz]gð?(R(R((sc:\py\lib\nmr.pytsratescCs9t|tƒo)t|ƒt|ƒjo|i|ijS(s>Return True if two traces have same timelines, False otherwise(t isinstanceR R R(Rtother((sc:\py\lib\nmr.pyt compatibleƒscCsAt|tƒp t‚n|i|ƒpt||ƒ‚ndS(s~ Raise a ValueError, if other is not a Trace, a SignalMismatchError if two traces are not compatible. N(RR RRR(RR((sc:\py\lib\nmr.pytcheck‡s cCst|i|iiƒƒS(sReturn a copy of the trace(R RRtcopy(R((sc:\py\lib\nmr.pyR!‘scCs&|i|ƒot|i|ijƒS(N(RtallR(RR((sc:\py\lib\nmr.pyt__eq__“scCs ||j S(N((RR((sc:\py\lib\nmr.pyt__ne__”scCst|i|i ƒS(N(R RR(R((sc:\py\lib\nmr.pyt__neg__–scCs|S(N((R((sc:\py\lib\nmr.pyt__pos__—scCsRti|ƒot|i|i|ƒSn|i|ƒt|i|i|iƒS(N(R RR RRR (RR((sc:\py\lib\nmr.pyt__add__™s cCsRti|ƒot|i|i|ƒSn|i|ƒt|i|i|iƒS(N(R RR RRR (RR((sc:\py\lib\nmr.pyt__sub__Ÿs cCs;ti|ƒot|i|i|ƒSntdƒ‚dS(Ns*a trace can be only multiplied by a number(R RR RRR(RR((sc:\py\lib\nmr.pyt__mul__¥scCs;ti|ƒot|i|i|ƒSntdƒ‚dS(Ns'a trace can be only divided by a number(R RR RRR(RR((sc:\py\lib\nmr.pyt __truediv__ªscCs5ti|ƒot|i||iƒSnt‚dS(N(R RR RRR(RR((sc:\py\lib\nmr.pyt__rsub__µscCs“t|tƒoF|i|ijo t‚nt|iti|i|ifƒƒSnt|iti|ititi|ƒdti ƒfƒƒS(NR ( RR RRR t concatenateRtarrayRR(RR((sc:\py\lib\nmr.pyt__and__ºs  )cCsR|djo|Snt|itititi|ƒdtiƒ|ifƒƒS(NR ( R R RR R,R-RRR(RR((sc:\py\lib\nmr.pyt__rand__Ás cCsDd|it|ƒ|i|idjodndt|iƒfS(NsTrace(dt=%.3es,%d points: %s)%stt (RR RRR trepr(R((sc:\py\lib\nmr.pyt__repr__ÆscCs t|iƒS(N(thashR(R((sc:\py\lib\nmr.pyt__hash__ÇscCs!|itti||iƒƒS(N(RtinttmathtfloorR(RR((sc:\py\lib\nmr.pyt __getitem__ÉscCs'||itti||iƒƒti|ht|ƒd<ti|id|ƒd<ƒdS(s<Save a trace in a binary format, sampling rate is not saved.RuR RZN(R\t savebinaryR2R RR(RR_RuR ((sc:\py\lib\nmr.pyRxrsc Cs|djo|djotdƒ‚nO|dj o|dj otdƒ‚n%|djot||iƒ}nt|ƒ}||jo |}n|djo|djo |}nO|dj o|dj otdƒ‚n%|djot||iƒ}n|djo d}nti||ƒ}|d}||}x¢tt|ƒƒD]Ž} | ||} | ||} | djod} |} n"| |jo||} |} nt|i | | !ƒt |i | | !ƒ|| Only one of 'Nwindow' and 'Twindow' arguments can be specifieds:Only one of 'Nstep' and 'Tstep' arguments can be specifiediiiN( R RR6RR R tzerosRYRGRtminR ( RtNwindowtTwindowtNsteptTsteptNtetNlefttNrighttnRIRJ((sc:\py\lib\nmr.pytenvelopevs@                2c Cs|djo|djo d}n|djo||i}n|djo d}n|t|ƒdjot|ƒd}nti|i| ƒ}|d|i}ti|i| ƒ}|iƒ|d|i}||||}|||}t|i|||iƒƒS(so Return an nmr.Trace object containing a straight line best fittin through first 'window' and last 'window' points (or first 'Twindow' and last 'Twindow' seconds). This can be subtracted from the signal to avoid ripple due to start and end level mismatch. If neither 'window' nor 'Twindow' is specified 'window' defaults to 1. iig@N( R RR R tmeanRRR R( RtwindowR|RVttstarttendttendtktb((sc:\py\lib\nmr.pytlinearbg¨s    cCs||i||ƒS(sl Return a difference between the trace and its linear background, see 'linearbg()'. (RŒ(RR†R|((sc:\py\lib\nmr.pytsubtract_linearbgÂscCst|iti|iƒƒS(s> Take a logarithm of every point of the trace (R RR R@R(R((sc:\py\lib\nmr.pyR@ÉscOs9ti|iƒ}ti|iƒ||i|||ŽS(s4 Plot the trace, only finite points (R tisfiniteRtpylabtplotR(Rtargstvargstcond((sc:\py\lib\nmr.pyRÏscOsFti|iƒ|idj@}ti|iƒ||i|||ŽS(s9 Plot the trace with log scale on y axis i(R RŽRRtsemilogyR(RR‘R’R“((sc:\py\lib\nmr.pytlogplotÖscCsh|djo7|djotdƒ‚nti||iƒ}nt|i||i|d|…ƒS(sK Return a subset of the trace at a different sampling rate sDownsampling is not specifiedN(R RR troundRR R(RR}tnewDTRI((sc:\py\lib\nmr.pyt downsampleÝs   N(6RRRR RRRRRRR R!R#R$R%R&R'R(R)R*t__div__t__radd__t__rmul__R+R.R/R3R5R9R;R<R>RDRURXRYt staticmethodR]RjReRqRsRrRwR tfloat32RxR„RŒRR@RR•R˜(((sc:\py\lib\nmr.pyR <sf                        +      2   RHcBseZdZd6d„Zd„Zd„Zd6d6d„Zd6d6d„Zd„Z d„Z d„Z d „Z d „Z d „Zd „Zd „Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„Zd„ZeZ eZ!eZ"d„Z#d„Z$d„Z%d „Z&d!„Z'd"„Z(d#„Z)e*d$„ƒZ+d6d%„Z,e*d&„ƒZ-d'e.i/d(„Z0d)„Z1d*d+„Z2d*d6d*d,„Z3d-„Z4d.„Z5d/e6d6d6d0„Z7d1„Z8d2d3„Z9d4„Z:d5„Z;RS(7s> A Fourier Transform of a signal. A spectrum can contain only a subset of frequencies to reduce amount of data. Frequencies are stored as 'f', complex spectral densities as 'w'. Spectra with identical sets of frequency can be added to, subtracted from, multiplied by and divided by each other using '+-*/'. 'self[f]' is the amplitude at frequency 'f'. IndexError is raised if f is not present in the spectrum. '&' can be used to combine two spectra without overlapping frequencies. ValueError is raised if there is an overlap. cCsÜ|djoctiti|dd…dfƒdtiƒ|_ti|dd…dfdtiƒ|_nit|ƒt|ƒjot dƒ‚ntiti|ƒdtiƒ|_ti|dtiƒ|_dS(sø Creates a Fourier Transform f - array of frequencies, only real component is used w - array of complex spectral densities. If a single argument is given, f[:,0] is frequencies, f[:,1] is spectral densities. NiR is2frequency and spectrum arrays are different length( R R RRRtft complex128twR R(RRžR ((sc:\py\lib\nmr.pyR÷s 4/$cCst|iiƒ|iiƒƒS(N(RHRžR!R (R((sc:\py\lib\nmr.pyR!scCst|i||i|ƒS(sR Return a subset of the Spectrum based upon 'condition' argument. (RHRžR (RRT((sc:\py\lib\nmr.pyRU scCs]|djo|iƒ}n|djo|iƒ}n|i|i|j|i|j@ƒS(s÷ Return a spectrum in given frequency range. If fmin is not specified or out of range, minimum frequency of the spectrum is used. If fmax is not specified or out of range, maximum frequency of the spectrum is used. N(R RLRMRURž(RRLRM((sc:\py\lib\nmr.pytfranges   cCs]|djo|iƒ}n|djo|iƒ}n|i|i|j|i|jBƒS(sé Return a subset of the spectrum excluding a frequency range limited by [fmin, fmax], boundaries being discared. fmin defaults to the minimum frequency, fmax defaults to the maximum frequency. N(R RLRMRURž(RRLRM((sc:\py\lib\nmr.pytnofranges   cCsšt|ƒdjo|Sn|i|ij}x]|D]U}ti|ƒo||i|jM}q4||i|dj|i|djBM}q4W|i|ƒS(s Return a subset of a trace, lacking frequencies mentioned in 'freq_blacklist'. The list should contain numbers - the frequencies to discard, and (fmin, fmax) two-number pairs, which are interpreted as frequency range boundaries. ii(R RžR RRU(Rtfreq_blacklistR“Rž((sc:\py\lib\nmr.pytcomb%s,cCs#||iƒjo||iƒjS(sj Return True if f is in the range of frequencies of the spectrum, False otherwise (RLRM(RRž((sc:\py\lib\nmr.pyt isinrange8scCs t|iƒS(sminumum frequency(RzRž(R((sc:\py\lib\nmr.pyRL?scCs t|iƒS(smaximum frequency(RGRž(R((sc:\py\lib\nmr.pyRM@scCs"|iƒ|iƒt|ƒdS(sfrequency stepi(RMRLR (R((sc:\py\lib\nmr.pytdfAscCsti|iƒS(sreal part of spectrum(RRR (R((sc:\py\lib\nmr.pytreCscCsti|iƒS(simaginary part of spectrum(RtimagR (R((sc:\py\lib\nmr.pytimDscCs t|iƒS(sabsolute value of spectrum(tabsR (R((sc:\py\lib\nmr.pyRªEscCs t|iƒS(N(R Rž(R((sc:\py\lib\nmr.pyRGscCs&t|tƒot|i|ijƒS(sZ Return True if two spectrums have same frequency arrays, False otherwise (RRHR"Rž(RR((sc:\py\lib\nmr.pyRIscCs'|i|ƒpt||ƒ‚ndS(sR Raise a SignalMismatchError if two spectrums are not compatible. N(RR(RR((sc:\py\lib\nmr.pyR OscCs>|iƒt|iƒƒj}|i|d|i|dfS(s½ Return a tuple containing the frequency and complex amplitude of the peak, defined as a point in the spectrum with maximum absolute value of the amplitude. i(RªRGRžR (RRR((sc:\py\lib\nmr.pytfindpeakVscCs|iƒdS(s4Return the frequency of a peak found by 'findpeak()'i(R«(R((sc:\py\lib\nmr.pytpeakf_scCs|iƒdS(s>Return the complex amplitude of the peak found by 'findpeak()'i(R«(R((sc:\py\lib\nmr.pytpeak`scCs>|iƒt|iƒƒj}|i|d|i|dfS(s½ Return a tuple containing the frequency and complex amplitude of the peak, defined as a point in the spectrum with minimum absolute value of the amplitude. i(RªRzRžR (RRR((sc:\py\lib\nmr.pytfindminbscCs?|i|ƒo/t|i|ijƒot|i|ijƒS(N(RR"RžR (RR((sc:\py\lib\nmr.pyR#kscCs ||j S(N((RR((sc:\py\lib\nmr.pyR$lscCst|i|i ƒS(N(RHRžR (R((sc:\py\lib\nmr.pyR%nscCs|S(N((R((sc:\py\lib\nmr.pyR&oscCsRti|ƒot|i|i|ƒSn|i|ƒt|i|i|iƒS(N(RRRHRžR R (RR((sc:\py\lib\nmr.pyR'qs cCsRti|ƒot|i|i|ƒSn|i|ƒt|i|i|iƒS(N(RRRHRžR R (RR((sc:\py\lib\nmr.pyR(ws cCsRti|ƒot|i|i|ƒSn|i|ƒt|i|i|iƒS(N(RRRHRžR R (RR((sc:\py\lib\nmr.pyR)}s cCsRti|ƒot|i|i|ƒSn|i|ƒt|i|i|iƒS(N(RRRHRžR R (RR((sc:\py\lib\nmr.pyR*„s cCs5ti|ƒot|i||iƒSnt‚dS(N(RRRHRžR R(RR((sc:\py\lib\nmr.pyR+‘scCsrt|tƒo^t|i|ijƒotdƒ‚ntti|i|iƒti|i|iƒƒSntS(Ns:Can't to merge two spectra with overlapping frequency sets(RRHtanyRžRR R,R (RR((sc:\py\lib\nmr.pyR.–s 5cCsBt|ƒdjo'dt|ƒ|iƒ|iƒfSndSdS(Nis&Spectrum [%d points in %g-%g Hz range]sEmpty Spectrum(R RLRM(R((sc:\py\lib\nmr.pyR3s'cCs5||jotdƒ‚n|i|i|jdS(Ns(frequency is not present in the spectrumi(t IndexErrorR Rž(RRž((sc:\py\lib\nmr.pyR9£s cCs7||jotdƒ‚n||i|i|j®scCs?ti|dddtdtƒ\}}}t||d|ƒS( sÁ Load trace in ASCII format: (1) Frequency [Hz] (2) Abs amplitude *** disregarded *** (3) Real part of amplitude (4) Imaginary part of amplitude Rpiiitunpacktkeep2Dyð?(iii(R\RqR^RH(R_RžtrRi((sc:\py\lib\nmr.pyRq°s *c CsGti||i|iƒ|iƒ|iƒfddd|dtƒdS(sÎ Save spectrum in ASCII format: (all in %.15e, tab-delimited) (1) Frequency [Hz] (2) Abs amplitude (3) Real part of amplitude (4) Imaginary part of amplitude Rts%.15eRuRvN(R\RwRžRªR§R©R^(RR_Ru((sc:\py\lib\nmr.pyRw¼sc Csti|dtƒ\}}}|d}t|ƒd}t|| ||d|!d|d|d|!ƒ}|djo3yt|htid<ƒ}Wq³h}q³Xnh}~xE|iƒD]7\}}y|i |ƒWqÃ|i ||ƒqÃXqÃW|S(sÒ Load a spectrum from a binary file. The dataset is assumed to be 3*N long, first N points - frequencies, next go the real parts and finally the imaginary parts of the spectrum. R[RZiiyð?itnan( R\R]R^R RHtevalR R´titemst__getattribute__t __setattr__(R_RbRcRdRRRŠ((sc:\py\lib\nmr.pyR]Æs$ 5  R0cCsetiti|i|iƒ|iƒgƒdtiƒ}ti|ht |ƒd<|d<ƒdS(sX Save the spectrum into a binary file. First all frequencies, then real and finally imaginary parts are stored in a single section of the file called 'channel0'. Optinally a header is saved (a string) Data format can be specified by 'dtype' argument, defaults to 4 byte floats. R RuRZN( R RR,RžR§R©RR\RxR2(RR_RuR Ro((sc:\py\lib\nmr.pyRxàs 9cOsL|idƒo|idƒ}nd}ti|i|iƒ|||ŽS(su Plot absolute amplitudes of the spectrum. Optional 'y0' argument shifts spectrum vertically ty0i(thas_keytpopRRRžRª(RR‘R’R¹((sc:\py\lib\nmr.pytplotabsísicOsO|itid|ƒ}tidƒtiti|ƒti|ƒ||ŽS(s„ Plot a hodograph of the spectrum - real on x and imaginary on y. Axis is set to proportional aspect ratio. yð?tequal(R R RCRtaxisRRR¨(RtphaseR‘R’tW((sc:\py\lib\nmr.pytplothodoøs cKsÓ|djo d}n|itid|ƒ}ti|iti|ƒ||d|}|djo|diƒ}n|i dƒo|i dƒnti|iti |ƒ||d|}||S(sˆ Plot real (solid) and imaginary (dash-dot) parts of the spectrum. Both are plotted in the same colour, either specified with 'color' argument, or picked by pylab automatically. Optional 'phase' argument rotates the spectrum Optional 'y0' argument shifts the spectrum vertically If 'label' is specified, only the real part is labelled. R0yð?t-itlabels--N( R R R RCRRRžRt get_colorRºR»R¨(RR¿tcolorR¹R’RÀtpretpim((sc:\py\lib\nmr.pytplotris , ,cCsSti|it||ƒjƒo't|tii|i||ƒƒSnt‚dS(sç Inverse FFT. Return nmr.Trace object. Only works if the spectrum is complete from 0 Hz to Nyquist Frequency, as if was produced by FFT of an 'N'-point trace with a sampling interval of 'dt' N( R R"RžRFR RDtirfftR tNotImplementedError(RRR((sc:\py\lib\nmr.pytiffts"'cCst|idd|iƒS(sÄ Shift frequencies to focus on 1-1.1MHz range In a returned spectrum 1 MHz is subtracted from all frequencies and frequencies are expressed in kHz, rather than Hz. g€„.Ag@@(RHRžR (R((sc:\py\lib\nmr.pytmhz'sicCs™|djo|iƒ}n|djo|iƒ}n|iti|i| ƒ|titi|it ƒdƒdj}|||j||j@S(sÛ Find peak frequencies. Peaks are those points which differ from neighbourgs by more than alpha times the rms absolute difference between the points. If 'singlepeaks' is True, a point is considered a peak only if it is higher that its both neighbours, otherwise points on sides of wider peaks are included as well. If 'minf'/'maxf' are specified, peaks are looked for only in a given frequency window. igà?N( R RLRMRžR\tabsdiffR R R…R^(Rtalphat singlepeakstminftmaxftpeaks((sc:\py\lib\nmr.pyt findpeaks/s  GcKs&|iti|i|i|ƒƒS(s§ Return a subset of the spectrum excluding single point peaks. For the peak search algorithm and argument meaning see nmr.Spectrum.findpeaks() (RUR t setmember1dRžRÓ(RR’((sc:\py\lib\nmr.pyt removepeaks@si cCs1ttiti|i|ifƒiƒ|ƒƒS(sg Thin the spectrum down by averaging every 'Nwindow' neighbour points together (RHR\taverageR R-RžR t transpose(RR{((sc:\py\lib\nmr.pyRÖGscCs"t|iti|i|iƒƒS(s¾ Evaluate an integral of the spectrum between the minimum frequency and every frequency present in the spectrum. Return the result as an nmr.Spectrum object. (RHRžR\t integrateR (R((sc:\py\lib\nmr.pyRØNscCs'y|i|iSWntiSnXdS(s‡ return the time domain trace voltage swing, if this information was saved into the spectrum or NaN otherwise. N(t trace_maxt trace_minR R´(R((sc:\py\lib\nmr.pyttrace_swing_VppVsN(<RRRR RR!RUR¡R¢R¤R¥RLRMR¦R§R©RªRRR R«R¬R­R®R#R$R%R&R'R(R)R*R™RšR›R+R.R3R9R;R<R>RœRqRwR]R RRxR¼RÁRÈRËRÌR^RÓRÕRÖRØRÛ(((sc:\py\lib\nmr.pyRHèsj                                        cCs tid|ddƒ||S(sÊ Return an array of frequencies for Real Fast Fourier Transform (only positive frequencies) N - number of points in the original time trace dt - sampling rate of the original time trace ii(R R(RR((sc:\py\lib\nmr.pyRF`s( RR R\RR7Rmt ExceptionRtobjectR RHRF(((sc:\py\lib\nmr.pyss     ÿ­ÿy